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Partial differential control theory and causality. (English) Zbl 0755.93048

New trends in systems theory, Proc. Jt. Conf., Genoa/Italy 1990, Prog. Syst. Control Theory 7, 599-605 (1991).
[For the entire collection see Zbl 0726.00023.]
From the author’s abstract: Classical control theory studies \(\text{INPUT}\to\text{OUTPUT}\) relations defined by systems of ordinary differential equations. Such a system is said to be causal if the knowledge of the input up to time \(t\) and initial conditions for output at time \(t_ 0<t\) are sufficient in order to recover the output up to time \(t\). A recent attempt to give a formal definition of causality for linear control systems has been done by J. C. Willems. The purpose of this paper is to extend this result to partial differential control theory, namely to the study of \(\text{INPUT}\to\text{OUTPUT}\) relations defined by (possibly nonlinear) systems of partial differential equations and relate it to delicate results on the symbol sequence of a linear partial differential operator.
Reviewer: E.Barron (Chicago)

MSC:

93C20 Control/observation systems governed by partial differential equations

Citations:

Zbl 0726.00023
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